Protesters have also accused the government of trying to change the military-backed constitution to cling to power.
Samak has denied the allegations.
Commenting on the border dispute with Cambodia, Suwit said he was concerned about the "sovereignty of Thailand" but did not elaborate.
Both countries have stationed soldiers near the disputed Preah Vihear temple since July 15, although they agreed in principle on Monday to move the 800 Cambodian troops and 400 Thais stationed in the area.
Border tensions intensified earlier this month after Unesco, the United Nations' cultural body, approved a Cambodian application to have the 11th century temple designated a World Heritage Site.